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Modular Representations of Finite Groups of Lie Type

Modular Representations of Finite Groups of Lie Type

£60.99

Part of London Mathematical Society Lecture Note Series

  • Date Published: December 2005
  • availability: Available
  • format: Paperback
  • isbn: 9780521674546

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  • Finite groups of Lie type encompass most of the finite simple groups. Their representations and characters have been studied intensively for half a century, though some key problems remain unsolved. This is the first comprehensive treatment of the representation theory of finite groups of Lie type over a field of the defining prime characteristic. As a subtheme, the relationship between ordinary and modular representations is explored, in the context of Deligne–Lusztig characters. One goal has been to make the subject more accessible to those working in neighbouring parts of group theory, number theory, and topology. Core material is treated in detail, but the later chapters emphasize informal exposition accompanied by examples and precise references.

    • This is the first comprehensive treatment of the representation theory of finite groups of Lie type over a field of the defining prime characteristic
    • Core material is covered in detail, while other topics and recent developments are surveyed
    • One goal has been to make the subject more accessible to those working in neighboring parts of group theory, number theory, and topology: chapters are accompanied by examples and carefully selected references
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    'This is the first comprehensive treatment of the representation theory of finate groups of Lie type over a field of the defining prime charecteristic.' L'enseignement mathematique

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    Product details

    • Date Published: December 2005
    • format: Paperback
    • isbn: 9780521674546
    • length: 248 pages
    • dimensions: 229 x 153 x 15 mm
    • weight: 0.34kg
    • contains: 30 tables
    • availability: Available
  • Table of Contents

    1. Finite groups of Lie type
    2. Simple modules
    3. Weyl modules and Lusztig's conjecture
    4. Computation of weight multiplicities
    5. Other aspects of simple modules
    6. Tensor products
    7. BN-pairs and induced modules
    8. Blocks
    9. Projective modules
    10. Comparison with Frobenius kernels
    11. Cartan invariants
    12. Extensions of simple modules
    13. Loewy series
    14. Cohomology
    15. Complexity and support varieties
    16. Ordinary and modular representations
    17. Deligne-Lusztig characters
    18. The groups G2
    19. General and special linear groups
    20. Suzuki and Ree groups
    Bibliography
    Frequently used symbols
    Index.

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    Modular Representations of Finite Groups of Lie Type

    James E. Humphreys

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  • Author

    James E. Humphreys, University of Massachusetts, Amherst
    James E. Humphreys was born in Erie, Pennsylvania, and received his AB from Oberlin College, Ohio in 1961, and his PhD from Yale University, Connecticut in 1966. He has taught at the University of Oregon, Courant Institute of Mathematical Sciences, New York University, and the University of Massachusetts, Amherst (now retired). He visits the Institute of Advanced Studies, Princeton and Rutgers. He is the author of several graduate texts and monographs.

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